The ornate shells of diatoms form between two membranes. In the normal algae cell the pattern is reminiscent of those formed by a Turing reaction-diffusion mechanism. However, we have found aberrant colonies whose shells have mutiply branching striae. These have given us a clue to the probable mechanism of striae growth. 1) The pattern of the striae can be explained by two growth rules: a) A stria which is too close to neighboring striae stops growing. b) A stria with too much room branches. Otherwise striae grow at their tips at a constant rate. 2) A model has been formulated for the growth and branching of a stria based on instabilities in diffusion limited growth of an amorphous precipitate from a supersaturated solution.